A NEW APPROACH FOR THERMAL RESISTANCE PREDICTION OF DIFFERENT COMPOSITION PLAIN SOCKS IN WET STATE (PART 2)

: Socks’ comfort has vast implications in our everyday living. This importance increased when we have undergone an effort of low or high activity. It causes the perspiration of our bodies at different rates. In this study, plain socks with different fi ber composition were wetted to a saturated level. Then after successive intervals of conditioning, these socks are characterized by thermal resistance in wet state at different moisture levels. Theoretical thermal resistance is predicted using combined fi lling coeffi cients and thermal conductivity of wet polymers instead of dry polymer (fi ber) in different models. By this modifi cation, these mathematical models can predict thermal resistance at different moisture levels. Furthermore, predicted thermal resistance has reason able correlation with experimental results in both dry (laboratory conditions moisture) and wet states.


Introduction
Consumers consider comfort as one of the most important attributes in their purchase of apparel products; therefore, companies tend to focus on the comfort of apparel products. Comfort is a pleasant state of physiological, psychological, and physical harmony between a human being and the environment [1]. Clothing comfort has two main aspects that combine to create a subjective perception of satisfactory performance: thermo-physiological and sensorial. The thermo-physiological relates to the way clothing safeguards and dissipates metabolic heat and moisture [2,3], whereas the sensorial relates to the interaction of clothing with the senses of the wearer [4,5]. Thermal-wet comfort being the strongest among tactile and pressure comfort perceived by subjects during exercise [6].
Dry heat transfer occurs through conduction, radiation, convection, and ventilation, whereas wet heat transfer when sweating includes several additional complex processes including evaporation, wicking, sorption and desorption, wet conduction (additional conductive heat transfer due to the clothing being wet), and condensation of moisture [7,8].
Thermal-wet comfort is mainly determined by the heat and moisture transport of fabric, which is related to fi ber characteristics as well as yarn, fabric construction, and fabric fi nish, recognizing that the extent of their relationship to comfort perception in clothing is also infl uenced by garment design, cut, and fi t. The basic thermal comfort properties are just two: thermal resistance (or insulation) and water vapor resistance (or permeability) [8]. Increasing moisture content in fabrics signifi cantly worsens their ability to transport water vapor. For wool fabrics and wool/viscose blended fabric, the value decreases by over 70-80%. However, in the case of the addition of polyester fi bers, the effective permeability of water vapor almost disappears, which is caused by substituting the air in pores by water with higher thermal conductivity. This means also that the physiological properties of the fabric, which is becoming increasingly wet as a result of use, are subject to sudden changes, which signifi cantly affects the quality of the apparel [9]. Oğlakcioğlu and Marmarali measured the thermal resistance of cotton knitted fabric in a wet state. Coolmax wetted fabric was used to simulate wetted skin. About 0.5 ml of water (containing detergent) was injected onto its surface and waited for 1 min for the liquid had been uniformly distributed within a circle of 45-50 mm. It was found that the wetted fabrics indicate lower thermal insulation and cooler feeling [10]. Clothing thermal insulation decreases during perspiration, and the amount of reduction varies from 2 to 8%, as related to water accumulation within clothing ensembles [11]. Another study on footwear reported about 19-25% (30-37% in toes) reduction of thermal insulation during sweating [12]. Kuklane et al. measured the effect of different sweat rates on thermal insulation and found a strong negative correlation. Furthermore, they found that 30% of the total moisture can stay in socks [13]. Thermal manikin results of dry and wet heat loss are presented from different laboratories for a range of two-layer clothing with similar dry insulations but different water vapor permeabilities and absorptive properties. For each climate, total wet heat loss is predominately dependent on the permeability of the outer layer. At 10°C, the apparent evaporative heat loss is remarkably higher than expected from evaporation alone (measured at 34°C), which is attributed to condensation within the clothing and increased conductivity of the wet clothing layers [14]. The characterization of insulation in wet states is very critical. There are many experimental and prediction models available to fulfill this need. Some researchers employed artificial neural networks (ANNs) models for thermal resistance predictions [15,16]. Hes and Loghin assumed thermal resistance of textile linked parallel to the thermal resistance of water in their suggested mathematical model [ 17 ]. Dias and Delkumburewatte's mathematical model predicted higher thermal conductivity than experimental [ 18 ] . In the thermal resistance model of Matusiak, all the multilayered fabric assemblies can be defined as cuboids filled with randomly oriented infinite cylinders (fibers). Conductive heat transfer can be calculated by analogy to electrical resistance and Fricke's law [ 19 ] . In most of the studies, thermal resistance is predicted by statistical models [16,17]. Mangat et al. presented a mathematical model for thermal resistance in the wet state with the series and parallel combinations of air, fiber, and water resistance. Their predictions are in good correlation with experiments by model-3 (air and fiber resistance in series, water in parallel) for denim fabrics while model-5 (R a and R w in parallel arrangement and R f in series) and model-7 (R f and R w in serial arrangement and R a in parallel arrangement) for weft knitted fleece fabric of differential fiber composition [18,19]. Hollies and Bogaty have suggested a parallel combination for measuring the effective thermal conductivity of moisten fabric by combining the volume fraction and thermal conductivity of water and polymer [20]. Naka and Kamata suggested three parameters (air, water, and polymer) model with the combination of parallel and series arrangements [21]. The problem with Mangat's models that they assumed the filling coefficient or conversely porosity as constant components. But they are changed with the changing of moisture levels because water has a different density. Their second assumption that the air is replaced by water is also not correct because of even >200% moisture content air still present in the fabric. A mathematical model for thermal resistance prediction, suggested by Wei et al. [22], is also very simple like Mangat's model. But they considered only fiber and air resistances. They ignored the water content. Their recommended model has fiber and air in series plus air in parallel. Hollies and Bogaty have ignored the series arrangement and their calculation for water volume presented in the fabric is also not clear. Naka and Kamata suggested three parameters (air, water, and polymer) model that was a good attempt but not conclusive, that is, use series, parallel, or combination of both.
Although there are enough prediction models available for different fabrics, these models are very complicated and limited to dry states. So the present research aims to measure the thermal resistance by different skin models and find or develop a simple mathematical model for thermal resistance prediction based on available physical parameters especially in wet states for socks with differential fiber composition.

Materials
All the socks samples have been knitted on the same machine (Lonati 144N 4'') settings by varying the main yarns to get the homogeneous samples with respect to specs and stretches for contrast comparison. After knitting, all the samples were processed for washing in the same machine bath followed by tumble drying and boarding.

Alambeta
Thermal resistance (R ct ) assessed using the Alambeta tester [23], which enables fast measurement of both steady-state and transient-state thermal properties. This instrument simulates, to some extent, the heat fl ow q (Wm −2 ) from the human skin to the fabric during a short initial contact in the absence of body movement and external wind fl ow. Thermal resistance (R ct ) (m 2 KWˉ1) is used to express the heat insulation properties of a fabric. R ct of textiles is affected by fi ber conductivity, fabric porosity, and fabric structure. It is also a function of fabric thickness, as shown by the following expression: (1)

Theoretical models
All the theoretical models for thermal resistance prediction are used by feeding the wet fi bre thermal conductivity ( prediction are used by feeding the wet fi bre thermal ) and fi lling coeffi cient ( wet polymer F ) of wet polymer instead dry and amended accordingly except Mangat's model. wet polymer F and of wet polymer instead dry and amended accordingly except are calculated as per Eqs (11)-(13). After this amendment, these models can also predict thermal resistance for wet fabrics.

Fricke's modifi ed model [24]
Thermal conductivity of fi brous material whose fi bers are perpendicular to the heat fl ow can be determined by the following equation: (2) λ fab = Fabric thermal conductivity, λ wet polymer = Wet fi bre thermal conductivity, λ a = Air thermal conductivity, F wet polymer = Fiber fi lling coeffi cient + Water fi lling coeffi cient, and F a = Air fi lling coeffi cient.

Ju Wie modifi ed model
Wie et al. [22] have divided the fabric basic unit into three parts in heat transfer fi eld: part I is composed of solid fi bers, part II is the porosity vertical to the heat fl ow direction, and part III is the porosity parallel to the heat fl ow direction, as shown as Figure 2. Fabric thermal resistance depends largely on the heat transfer process in the basic unit. In this model, heat fl ow considered through the fabric in a combination of fi ber and air in series plus air in parallel.

Suggested amendments and calculations
By assuming that fabric density is changing with wetting, which causes to change the fi lling coeffi cient, porosity, and thermal conductivity of the fabrics. Based on these assumptions, the following three equations are developed that will be used to fi nd the fabric density, fi lling coeffi cient, and thermal conductivity for different moisture levels. Average thermal conductivity for different fi bers (within socks) at different moisture levels will be calculated as per Eq. (11): (11) F w = Water fi lling coeffi cient, F fi b1 = First fi ber fi lling coeffi cient, F fi b2 = Second fi ber fi lling coeffi cient, F fi b3 = Third fi ber fi lling coeffi cient, λ w = Water thermal conductivity, λ fi b1 = First fi ber thermal conductivity, λ fi b2 = Second fi ber thermal conductivity, and λ fi b2 = Third fi ber thermal conductivity.
The fi lling coeffi cients for water, fi ber, wet polymer, and air are calculated as per below steps: Air fi lling coeffi cient ( a F ) is calculated as per the following Eq.
Filling coeffi cient for wet polymer will be calculated as per Eq. (13). This value will be used as input in all the above models for the measurement of thermal resistance in wet states.
(13) 2.3.4. Schuhmeister's modifi ed model Schuhmeister [28] summarized the relationship between the thermal conductivity of fabric and the fabric structural parameters by the following equations: where is the thermal conductivity of fabric, is the conductivity of wet fi bers, is the thermal conductivity of fabric, is the conductivity of air, wet polymer F is the fi lling coeffi cient of the solid fi ber, and a F is the fi lling coeffi cient of air in the insulation.

Militky's modifi ed model
Militký and Becker [29] summarized the relationship between the thermal conductivity of fabric and the fabric structural parameters by an empirical equation: where is the thermal conductivity of a fabric, is the conductivity of wet fi bers, is the thermal conductivity of a fabric, is the conductivity of air, wet polymer F is the fi lling coeffi cient of the solid fi ber, and a F is the fi lling coeffi cient of air in the insulation. resumed their dry (lab conditions) R ct after 6 h of conditioning. P2, P6, and P7 could not resume their thermal resistance even after 8 h. P5 (polypropylene) has the highest moisture loss or evaporation rate followed by P6 (wool) and P3 (polyester). P1 (cotton) and P2 (viscose) are the worst ones. P4 (nylon) and P7 (acrylic) fallen in the middle. Predicted (by different models) and experimental thermal resistance is given in Table 4. For all the models, the input thermal conductivity and fi lling coeffi cients were measured for wet polymer at different moisture levels.
The correlation between experimental and predicted models is checked by r 2 value. The values of coeffi cient of determination for all the models showed that these models can make reasonable predictions of thermal resistance in dry as well as The output of Eqs (11)-(13) is used as input in all the above models. So with the combinations of suggested and abovementioned models, thermal resistance at different moisture levels will be predicted. The thermal conductivity of water and air is taken as 0.6 and 0.026 Wm -1 K -1 , respectively, while the density of water is 1000 kgm -3 . The values of the different input parameters used in this study are given in Table 3 [30].

Statistical analysis
Theoretical and experimental results are statistically analyzed by the coeffi cient of determination (R 2 ) and the sum of squares of deviation (SSD). Correlation graphs are drawn through scatter diagrams in Microsoft excel. The following are the equations behind the calculation of (R 2 ) and SSD [31].

Results and discussion
Sock samples were tested for a relative cooling effect, thermal resistance, and thermal absorptivity in the dry state (laboratory conditions moisture content). Then, wet to saturated level (70% moisture content) by BS EN ISO 105-X12 standard test method. Establish technique for preparing wet fabric of a known ovendry weight of the fabric, then thoroughly wet out it in distilled water. Bring the wet pick-up to 70 ± 5% by putting wet testing fabric on a blotting paper. Avoid evaporative reduction of the moisture content below the specifi ed level before the tests are run. Furthermore, tested again after 2, 4, 6, and 8 h of conditioning successively in laboratory standard environmental conditions at known moisture level.

Effect of moisture on thermal resistance (m²KW -1 )
As mentioned earlier, dry and wet socks with differential moisture content were checked on Alambeta. The Alambeta is selected to avoid the effect of convection. Figures 3-11 demonstrated that as the moisture (%) increased thermal resistance decreased and vice versa irrespective of sock fi ber composition or structure. Only P3, P4, and P5 socks have    Fricke has overall top thermal resistance prediction generally at 3%, 6%, 36%, and 52% moisture level specifically for P4 (nylon 70%, polyester 26.54%, and elastene 2.63%) as shown in Figure 6 followed by Ju Wie and Maxwell. Militký again got the lowest position. Schuhmeister on the second number from the lower side. This is also verified from SSD values, that is, 0.0000382, 0.0000797, 0.0000901, and 0.000404 for Fricke, Ju Wie, Maxwell, Schuhmeister, and Militký, respectively.
In Figure 7 for P5 (polypropylene 65.22%, polyester 31.65%, and elastene 3.13%) sock, Schuhmeister and Maxwell's prediction is the best among all other models with less SSD, that is, 0.0000286325 and 0.000031 with respect to experimental thermal resistance. Then, Ju Wie (SSD = 0.0000887) followed by Militký (SSD = 0.000101) and Fricke (SSD = 0.000115). Figure 8 shows the effect of moisture content (%) on the thermal resistance of P6 sock (wool 76.19%, polyester 21.67%, and elastene 2.14%). P6 sock could not resume its dry state moisture content and ultimately thermal resistance after 8 h of conditioning due to its hydrophilic nature. 7.43% moisture content is due to the presence of polyester fiber in the composition in the dry state. All the models have a reasonable prediction of thermal resistance as evident in Figure 8. the wet state also at different moisture levels for all the major fiber blends being used for socks.
The predicted and experimental thermal resistance of P1 (cotton 80%, polyester 18.20%, and elastene 1.8%) at various moisture levels is given in Figure 3. Maxwell model has the best prediction at 10.1%, 20.61%, 61.17%, and 67.02% moisture levels followed by Frick, Schuhmeister Militký, and Ju Wie. P1 sample has still about 21% moisture content after 8 h of conditioning due to the higher composition of cotton fiber content (80%).
In the case of P2 sock (viscose 81.08%, polyester 17.22%, and elastene 1.77%), the almost same trend is observed as well as moisture loss is concerned after consecutive periods of conditioning as shown in Figure 4. Maxwell and Fricke have the best thermal resistance prediction at all moisture contents. Schuhmeister and Militký have a good prediction at 43.83%, 57.88%, and 64.46% moisture contents. Militký has the best prediction at 44%, 58%, and 64% moisture content. Ju Wie has a better prediction where the moisture level is less than 20%.
P3 sock (polyester 98.38% and elastene 1.62%) has the highest moisture loss (evaporation rate) due to polyester hydrophobic nature after successive periods of conditioning as shown in Figure 5. Militký's model's prediction is a bad one among all the models. Overall, Fricke has the best prediction

Conclusion
By adopting the new approach of feeding wet polymer filling coefficient and thermal conductivity instead of dry polymers, different models can make a reasonable prediction of thermal resistance in wet states as well. All the models have a coefficient of determination (R 2 ) >0.78.
Polymer filling coefficient remains constant while water and air filling coefficients are changing with the variation of moisture which leads to change the thermal conductivity.
P3, P4, and P5 socks samples have resumed their dry (laboratory conditions) R ct after 6 h of conditioning. P1, P6, and P7 could not resume their insulation even after 8 h of conditioning.
This study was conducted after successive periods of intervals to monitor the evaporation rate as well. So that many moisture contents (%) point missed in the graphs for some samples. The next study could be planned to test controlled moisture [32].